goals

A boy multiplied $$987$$ by a certain number and obtained $$559981$$ as his answer. If in the answer both $$9$$ are wrong and the other digits are correct, then the correct answer would be:

When a natural number $$n$$ is divided by $$4$$, the remainder is $$3$$. What is the remainder when $$2n$$ is divided by $$4$$?

Consider the following statements:

A number $${ a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 }{ a }_{ 5 }$$ is divisible by $$9$$ if

1. $${ a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 3 }+{ a }_{ 4 }+{ a }_{ 5 }$$ is divisible by $$9$$.

2. $${ a }_{ 1 }-{ a }_{ 2 }+{ a }_{ 3 }-{ a }_{ 4 }+{ a }_{ 5 }$$ is divisible by $$9$$.

Which of the above statements is/are correct?

A number $${ a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 }{ a }_{ 5 }$$ is divisible by $$9$$ if

1. $${ a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 3 }+{ a }_{ 4 }+{ a }_{ 5 }$$ is divisible by $$9$$.

2. $${ a }_{ 1 }-{ a }_{ 2 }+{ a }_{ 3 }-{ a }_{ 4 }+{ a }_{ 5 }$$ is divisible by $$9$$.

Which of the above statements is/are correct?

Using divisibility tests, determine which of the following numbers are divisible by $$10$$:

(a) $$54450$$ (b) $$10800$$ (c) $$7138965$$ (d) $$7016930$$ (e) $$10101010$$

(a) $$54450$$ (b) $$10800$$ (c) $$7138965$$ (d) $$7016930$$ (e) $$10101010$$

$$24 P$$ leaves remainder $$1$$ if it is divided by $$3$$ and leaves remainder $$2$$ if it is divided by $$5$$.

Find the value of $$P$$